Scaling law for defining the relativistic shift of the high field side electron cyclotron emission diagnostics on the tokamak device

Our previous work [X. Yu et al., Rev. Sci. Instrum. 93, 083518 (2022)] demonstrated that high field side (HFS) electron cyclotron emission (ECE) diagnostics can effectively measure electron temperature (T) information in the harmonic overlap region, where the electron distribution follows a Maxwellian. However, this requires relativistic shift corrections, which can be provided by simulation codes. Using a synthetic ECE code, we performed a statistical analysis to examine the relationship between relativistic shifts and plasma parameters, including T, electron density (n), magnetic field (B), and major radius (R0). For the first time, we proposed a scaling law for the relativistic shift in HFS ECE diagnostics, enabling direct calculation of these shifts from diagnostic data. Simulation results from both HL-3 (Huan Liu Qi-3) and ITER (International Thermonuclear Experimental Reactor) plasmas showed that this scaling law agrees well with simulated relativistic shifts (DR), even under varying pedestal heights. Furthermore, applying this scaling law, we demonstrated that it can provide results nearly identical to the preset T, even at the right-hand cutoff in high densities ITER plasmas. Finally, qualitative simulations suggest that HFS ECE can accurately localize the position of the neoclassical tearing modes (NTMs). The introduction of this scaling law represents a significant advancement in the practical application of HFS ECE diagnostics for measuring T profiles. It is expected to enhance the capabilities of ECE in high-β, high-density plasma scenarios.